Multiple own rates of interest don't matter, but the monetary policy target does matter

There are lots of problems with thinking about monetary policy as setting a nominal rate of interest, and trying to keep the actual real rate of interest equal to the natural real rate of interest. But multiple own rates of interest (the "Sraffa problem") isn't one of them.

Suppose Canada produces and consumes apples and bananas. Suppose the Bank of Canada wants to target 2% inflation. And it wants to do this by setting an appropriate nominal rate of interest. Unless the relative price of apples and bananas never changes, and is never expected to change, any given nominal rate of interest will mean a different real own rate of interest on apples than on bananas. But so what?

There will be one time-path of the nominal rate of interest that is compatible with* keeping the inflation rate on apples exactly at 2%. But the Bank of Canada does not know what it is. And if the Bank of Canada ever gets off that "warranted" time-path, which it will, because it doesn't know in real time what it is, that warranted time-path will shift. Because monetary policy has real effects on savings and investment, as well as nominal effects on actual and expected inflation.

And there will be a quite different time-path of the nominal interest rate that is compatible with keeping the inflation rate on bananas at exactly 2%. It is quite a different time-path because all sorts of real shocks and real trends will cause the relative prices of apples and bananas to change over time. And if the Bank of Canada ever gets off that warranted time-path, that warranted time-path will shift, and it won't necessarly shift in the same way that the warranted time-path for keeping apple inflation at 2% would shift. Because monetary policy will have real effects, including real effects on the relative supply, relative demand, and relative price, of apples and bananas.

And there will be a third warranted time path for nominal interest rates, different again from the first two, if the Bank of Canada decides to target 2% inflation on a weighted average of the prices of apples and bananas, according to their weights in the CPI. And it too will shift differently from the first two warranted time-paths if the Bank of Canada ever misses that warranted time-path.

Look. Trying to keep the actual interest rate equal to the warranted interest rate is a problem. Because the Bank of Canada does not know what the warranted rate is, so will miss it, and because it doesn't know how its own misses will shift that warranted time-path.

But once the Bank of Canada has decided what price index it wants to target, the fact that targeting a different price index would mean it would be trying to solve a different problem with a different solution isn't itself a problem. Because it's not trying to target a different price index.

Multiple own rates of interest would only be a problem if the Bank of Canada decided to change its target price index. If it decided to switch from a 2% CPI inflation target to a 2% GDP deflator target, for example. It would have to change to a different time path for nominal interest rates. It would have to change how it responded to the consequences of its own past mistakes. And the Lucas Critique reminds us that the old empirical correlations and rules of thumb it had learned from experience under the old monetary regime might change or not work as well under the new regime. In fact, those old empirical correlations and rules of thumb could only be simply translated for use in the new monetary regime if money were always and everywhere neutral and superneutral, in the short run as well as the long run. And it isn't. Because if it were, then central banks could not use interest rate policy in any case, because the price level would be indeterminate.

Natural rates are a theoretical construct. Natural rates exist in natural rate models. A natural rate model is a model in which, in some sense (normally a "long run" sense), monetary policy is neutral and superneutral, so that some real variables in that model are invariant to some parameters (like the mean levels and mean growth rates of nominal variables) of the monetary policy regime.

What long run neutrality and superneutrality would imply, and what the meaningfulness of the natural rate concept does require, is that if the Bank of Canada had always been targeting 3% CPI inflation instead of 2% CPI inflation, the warranted time-path for the nominal interest rate in that counterfactual world would be everywhere 1% above the warranted time-path under a 2% CPI target. It's a very simple translation from one to the other. If that isn't true, then money is not superneutral, and you can't meaningfully speak of natural real rates that are independent of long run inflation. But comparing a 3% CPI target with a 2% CPI target is very different from comparing a 2% apple price target with a 2% banana price target.

In a natural rate model, there may be a natural rate of unemployment, a natural rate of output, a natural relative price for apples and bananas, and a natural real rate of interest. And they will all be changing over time, in response to real shocks and trends. Or, rather, there will be a whole vector of natural rates of unemployment, for all the different types of workers. And a whole vector of natural rates of output, for all the different types of goods. And a whole vector of natural rates of relative prices, for all the different goods. And a whole vector of natural real rates of interest too, measured in terms of all the different goods. And they will all be changing over time, in response to real shocks and trends.

So what if natural rates are a vector? Or rather, a matrix? If your monetary policy misses one, you almost certainly miss them all. And if your monetary policy hits one, it almost certainly hits them all. ("Almost certainly", because the relationship between those variables and monetary policy may not be monotonic.) Pick one, and try to hit it, if you must, and if you can. [Update: That bit was maybe a bit misleading, because it looks like I'm saying it doesn't matter what target the central bank picks. See my reply to J.V. Dubois below.]

Better yet, don't try. Forget real variables, even as very short run targets for monetary policy. Target a nominal variable. Like NGDP. It's got $ in the units. And central banks ultimately only control the $ unit.

(*Notice I carefully said "compatible with keeping the inflation rate at 2%", rather than "causing the inflation rate to stay at 2%". That's because of the indeterminacy problem. An equilibrium path for the price level implies an equilibrium path for the nominal interest rate, but the reverse is not true.)

david. Yep. But that's OK. If money isn't neutral, or super-neutral, in any sense then natural rates don't exist. We don't need differences in own rates of return (something that would generally be true under barter as well as monetary exchange) to tell us that. The difference in own rates of return between apples and bananas adds nothing to the debate about neutrality or superneutrality.

I was thinking about adding an addendum to the post: Saying that natural rates don't exist because the natural rate on apples is different from the natural rate on bananas is like saying that Friedman destroyed the natural rate theory by saying that the natural rate of unemployment is different from the natural rate of interest.

Interesting post, Nick, but I think you are being too cute here. I am quite sure people like Daniel Kuehn are misinterpreting the significance of what you're saying.

When you say the difference in own-rates doesn't matter, you do NOT mean, "So Hayekians can relax, they are safe from Sraffa's attack." No, what you mean is, "This is the least of the Hayekians' worries. Even putting aside Sraffa's observation, there is no such thing as 'the' natural rate of interest that serves as a non-boom-inducing target for the central bank when setting nominal interest rates." Right?

In case you don't know the context, I have been telling Austrians for years that Lachmann in no way defended Hayek from Sraffa, when he (Lachmann) pointed out that once you specify a good as the numeraire, then arbitrage ensures a uniform rate of return quoted in that good, across any other good. So I am worried that such Austrians will read this post by you, and say, "This is really complicated stuff, and I never quite understood Bob's tedious examples, but it turns out I don't have to wade through them. The wise Nick Rowe agrees with us Austrians that Sraffa had no point."

Bob: I am very pleased to see you here. I take my hat off to an Austrian, who thinks Sraffa was right against Hayek (on this point, anyway). Ironically, or coincidentally, I might add that I am disagreeing here with David Laidler, who, IIRC, thought that Sraffa was right against the Neo-Wicksellians. It's a mixed up old world, but it's good to see it mixed up like this sometimes. Not everything is the party line, of us against them.

I do not trust my knowledge of Hayek well enough to know if I am agreeing or disagreeing with him.

One point: we should stop defining the natural rate (of anything) as the rate that would exist in a barter economy. A barter economy would be so different in so many ways than a monetary exchange economy, I wouldn't know where to start. (Actually, a barter economy might still be back in the stone age!) Natural rates, if they exist, exist only in a certain class of models. They exist in reality only insofar as those models represent reality. As to whether those models do represent reality, the answer, as with all models, can only be "up to a point". Or maybe "up to a point, Lord Copper"!

'No, what you mean is, "This is the least of the Hayekians' worries. Even putting aside Sraffa's observation, there is no such thing as 'the' natural rate of interest that serves as a non-boom-inducing target for the central bank when setting nominal interest rates." Right?'

Wrong. I think. I think there is such a thing as a time path for the nominal interest rate that would be compatible with a non-boom-inducing policy for the central bank. And by extension, there exists a time-path for any real rate of interest, defined as that nominal rate minus the inflation rate on that same particular good, or index of goods, that would be compatible with non-boom-inducing monetary policy. And if money is long-run superneutral, that real rate would be invariant with respect to the long run mean inflation rate.

I would tentatively define "non-boom/slump inducing" with reference to the indeterminacy problem, but I can't figure out the right words to do it.

Price indexes are generally not invariant to the path of quantities or to the distribution of income unless preferences are homothetic. So, targeting prices levels or NGDP levels will NOT make the economy "as if" money is neutral. Please give up, money is always and everywhere not neutral. As with Friedman's dictums--either they were wrong or they were banal or already discovered by other people (such as Joan Robinson's inflation barrier packaged as NAIRU).

srini: if I thought that monetary policy did not have some real effects I wouldn't care about monetary policy at all, and wouldn't spend all my time debating what the best monetary policy is. I would hand the keys to the Bank of Canada to a bunch of monkeys, knowing it wouldn't make any difference to anything that mattered.

Hang on a second. It's one thing to say "there exists a nominal rate of interest that the central bank can set, such that it avoids causing an inflationary boom." It's quite another thing to say, "And this particular nominal interest rate--or path of nominal interest rates over time--is equal to a 'real' rate that can somehow be derived from an analysis of all the non-monetary conditions in the economy."

So not to be too pedantic here, but I think you really should be agreeing with the position I attributed to you.

Bob: I'm not quite sure what you are asking here. But if you wrote down a model, in which money was "long run" neutral and super-neutral, then by definition I (or I plus a bunch of mathematicians) would be able to solve that model for a set of real variables that were invariant wrt any scalar multiple of the time path of the level of any one nominal variable (neutrality), and invariant wrt any scalar multiple of the time path of the growth rate of that same nominal variable (super-neutrality). In other words, we wouldn't need to know the central bank's target for the price level, or the target rate of inflation, to derive those real rates. (But those real rates would generally not be invariant with respect to the variance and covariances of monetary policy).

Hayek: To avoid an unsustainable boom, the central bank should set the nominal interest rate equal to the natural rate, i.e. the rate that would exist if there were no money and capital goods traded against consumption goods in kind.

Sraffa: If relative exchange ratios change over time, there is no such "natural" rate. You can't look at a barter economy and derive "the" natural rate of interest.

Lachmann: Hayek threw in the towel too quickly. You just pick a commodity as the numeraire, and boom, arbitrage ensures that all investments yield the same rate of return, measured in that commodity. So *that's* the natural rate the central bank should pick.

[Decades later.]

Bob Murphy: That is stupid. That doesn't work at all. If you pick a different commodity, "the" rate changes. So we're back to Sraffa's original problem. We still are no further along, than in Hayek's response to Sraffa when he gave a hint of an answer but not the full-blown reply.

Modern Austrians: No Bob, Sraffa did not like the free market. Clearly he was wrong, and we are suspicious that you don't see this.

Nick Rowe: Sraffa's "Problem" isn't a problem at all.

Modern Austrians: See Bob! Even the socialist Canadians agree with us.

You know it could be a fun and entertaining educational series on the thoughts of competing economic schools if you were to write a bunch of those exchanges in that style (of course being fair to all sides).

Nick (posing as rabid Canadian socialist): all the above are wrong, but some mix of Bob Murphy and Lachmann comes closest. Suppose (just to keep it simple) the Bank wants 0% inflation. The question is, which of many possible inflation rates does it want to target to 0%? Apples, bananas, the CPI, or what? And how it answers that question matters (unless all prices are perfectly flexible etc. so that money is perfectly neutral even in the short run). But once the central bank has answered that question, the rest of Lachmann's answer is fine. Suppose the Bank decides it's best to target the CPI, then it must (try to) set the nominal rate of interest equal to the natural rate on the CPI basket. Suppose instead the Bank decides it's best to target the price of apples, then set the nominal rate equal to the natural rate on apples. Etc.

Yep, the real problem, oh Modern Austrians, is what do you mean by "non inflationary"? Do you mean non-apple inflationary? Non-banana inflationary, or what? Which is the best sort of "non-inflationary" to have?

Okaaay, Nick, but all the stuff about "arbitrage ensures a single real rate of return, measured in a given numeraire" is distracting. When Sraffa said, "Heh heh Friedrich, there are many own-rates of interest, so which one should we pick?" then Hayek should have just said--anticipating Nick Rowe--"The right one."

Nick: "we should stop defining the natural rate (of anything) as the rate that would exist in a barter economy. A barter economy would be so different in so many ways than a monetary exchange economy, I wouldn't know where to start."

Tonto: "What you mean we, Paleface?"

I really wish you would stop using that term: barter economy. AFAICT you usually mean a Walrasian economy. So why not say that instead? If the pedants insist on Arrow-Debreu economy that's fine too.

Kudos to Bob Murphy for the most entertaining comment I've seen in a while.

Multiple commodity rates of return? I could be horribly wrong but I was thinking Hicks/Tobin solved all of this with the expectations structure of interest rates, separation theorems and GE CAPM, using money itself as the numeraire, of course. The risk free asset is by definition *the* numeraire - how can there be any other? Hayek/Lachmann's logic is not sufficiently neo-Wicksellian and hence looks vulnerable to the Sraffa/Murphy critique but individual commodity numeraires make no sense in the aggregate. And arbitrage logic between *all* commodities is not even a necessary argument for this. Arbitrage logic removes the relative price distortions between commodities in equilibrium, with perfect information and complete markets and no false trading. Let go of equilibrium and relative price distortions may yet persist. The term structure of interest rates can be out of whack. So can the 'commodity structure' of interest rates. This limits what a central bank can possibly achieve (which is ok, now we're in the territory of optimal allocation of resources rather than just preventing booms and busts) and still leaves Minsky's challenge of the dissonance between the two price levels (commodity prices and asset prices) but the central bank can still *minimize* the problem of involuntary employment (or accelerating inflation) by at least clearing the market for the risk free real rate. And involuntary unemployment and accelerating inflation are pretty much the only real or nominal phenomena that we really want to prevent.

Plus, Sraffa's logic is the classic pre-expectations type thinking. If the central bank is targeting what everybody thinks/wants/expects it to target (and the economy is in Leikjonhufvud's corridor), then Sraffa's logic falls apart, even if that target is not *the* numeraire.

But yes, I agree with Nick. Trying to target real variables is a tricky job. The aim is to so broadly clear interest rates while holding on to a nominal anchor. I'd still go for some measure of the price level rather than total nominal spending, but one that's reflective of producer prices rather than consumer prices, ala Frankel. Nominal wage targeting seems best, though I don't know how that can be done. Mankiw had some ideas 10 years ago on what price index should a central bank be targeting. He thought it should include a huge weight on wages and salaries - http://www.economics.harvard.edu/faculty/mankiw/files/target.pdf

This is fascinatin article, thanks for the link to the discussion. Anyways I still need to clarify what was said in Nick's debate with Bob. Nick, you say this in the article: "So what if natural rates are a vector? Or rather, a matrix? If your monetary policy misses one, you almost certainly miss them all. And if your monetary policy hits one, it almost certainly hits them all. ("Almost certainly", because the relationship between those variables and monetary policy may not be monotonic.) Pick one, and try to hit it, if you must, and if you can."

So let's say that Bank wants to select one of the two possible own real rates of good: apples or bananas. So what you say is basically that even if the time path of the nominal interest rates will look completely differently based on what commodity is selected to guide monetary policy, it is the changes in nominal interest rates that are important in steering the economy. So if we assume that Bank would be able to stick to the own natural rate if any of those commodities, it would be by extension be able to ensure that every commodity has the right natural rate of interest?

But what your point is that it is not a problem that nominal interest rate path set by the Bank would be different if we target different own natural rates of different commodities (or basket of commodities etc.). It is the mistakes that Bank does that are truly the problem, because bank does not know the own natural rate of target commodity in advance and more importantly, expected real rates even if "corectly" captured (such as using market futures as MM want to do for NGDP) will already incorporate past mistakes into the calculation so they may not be identical with NATURAL rates for the comodity that was selected to guide monetary policy? Do I understand this correctly?

So what you say is - stick with the nominal target and let the real rate be determined by markets. The job of the CB is not to keep the economy on some matrix of natural rates for comodities, but to construct such a nominal target that offsets real impacts of nominal changes - like sticky prices, downward wage rigidity and possibly other things - like impact of inflation on investment due to taxes on capital etc.

I get the real variable as a lagging indicator encompassing things like capital stock, R+D, employment, education, laws....it is trackable but might not be worth it. The money goes to a bank, not a researcher who has an idea to put trees (that might float) under peat moss as a sequester. Even if you perfect the measure of industrial growth with which to perfectly match an interest rate, it will be of only limmited utility to those who would be the highest ROI recipients of cash. Stuck with finance and petro for some time here. Defence and health insurers south...

But the history of economic thought would have been much simpler if Sraffa (or anyone) had said to Hayek: "Which inflation rate do you want to keep at zero? Gold? Silver? Copper? Apples? Bananas? Wages? The CPI?". He didn't need to mention natural rates at all. The question of which inflation rate you want to target (assuming it is some inflation rate you want to target, rather than the money stock or NGDP or something) makes sense whether or not natural rates even exist.

Though, what is strange to me is that that debate was presumably taking place against the backdrop of the gold standard, when everyone automatically assumed that the inflation rate on gold would be what the central bank targeted. So, unless someone advocated abandoning the gold standard in favour of the CPI standard or something, which AFAIK they didn't, what was the debate even about??? Was it really about the Law of Reflux? Hmmm, thinking about that makes me realise I don't understand the history of thought at all.

Kevin: "Kudos to Bob Murphy for the most entertaining comment I've seen in a while."

Seconded. Plus it was very succinct and clear too. Bob must make a great teacher.

I did mean "barter" in this case, and not Walrasian, and I meant barter because, IIRC, Wicksell (in one of his definitions of the natural rate) said barter, not Walrasian. But yes, my "we" really meant "any of you guys who might, following Wicksell, still be thinking of defining the natural rate as that rate which would exist in a barter economy".

But on that same subject, it was Friedman who at one point defined the natural rate of unemployment as that which would exist in a Walrasian economy, but he added so many qualifications about embedding trading frictions into that Walrasian economy that: it wasn't really a Walrasian economy any more; it was close to vacuous. His real definition of the natural rate was a stipulative one, when he said the LR Phillips Curve was vertical at some rate, and called that rate the natural rate.

Ritwik: "Multiple commodity rates of return? I could be horribly wrong but I was thinking Hicks/Tobin solved all of this with the expectations structure of interest rates, separation theorems and GE CAPM, using money itself as the numeraire, of course."

I don't think you are wrong. But I think the basic point is simpler, and doesn't need CAPM and stuff. And I think the basic point is somewhere all in Keynes, and all in Fisher, and probably all in other economists too.

Picky point: I don't think you can say that money or the numeraire is by definition risk-free. The risk that matters is presumably consumption risk. There is an extension of CAPM (I've forgotten what it's called, but something like "CAPM Marginal Utility") that handles this.

Ritwik: just to be more clear: the CAPM is all about different interest rates because of different risk. The basic point about different own rates of interest on different goods can be made even where there is no risk. If (say) the nominal interest rate is 5%, the inflation rate on apples is 3%, and the inflation rate on bananas is 1%, then the real rate of interest in terms of apples is 2%, and the real rate of interest in terms of bananas is 4%.

JV: Hmmm. Maybe I wasn't very clear on that "Pick one.." bit, and ended up saying, or looking like I was saying, what I didn't mean to say.

Because it really does matter which good you pick to target the price of. Suppose the price of apples is sticky, and the price of bananas and all other goods is perfectly flexible. You should target the price of apples. Because the actual price of apples won't move quickly to the equilibrium price of apples, you need to use monetary policy to keep the equilibrium price of apples close to the actual price of apples. And if you succeed in keeping the equilibrium price of apples equal to the actual price of apples, you will hit all the natural rates of everything. And if you fail, you will (almost certainly) miss all the natural rates of everything.

I'm thinking about this in terms of individuals, motivations. If I make a peat moss R+D proposal and the Central Bank long-term thinking psychic is aware of this, he could lower rates a bit for me. But money is only part of my motivation. What I really need is things like awards, nicer parking spaces, better peat blogs/forums...there are different worker motivation ROIs where even if you get the dollar right, the interest rate right, it might not matter as much as other factors (growing or shrinking Crowns). I guess this means hitting the right apple rate is only a partial victory. And the further away from optimal your institutional capital is (suppose the apple workers don't get bathroom breaks and all get urinary tract disease), the less the victory is. I mention this because I think it can be measured, what Central Bank limits are. Maybe all the workers need from Carney is a personal "thank you"?

Nick: Ok, so I think I've got that part you said correctly. But the point is that if there bananas and apples would have equally sticky prices, but they would have different natural interest rates it does not matter which one we select. Of course nominal rates path would look differently, but ultimately the effect would be the same.

To be concrete, imagine that apples have natural rate of interest 2% and bananas are 3% and for next 10 years they will be stable forever. They are equally suitable for monetary policy targeting purposes, their prices are equally sticky. So if our goal is to have 0% inflation of whatever good we select, we could end up with either 2% nominal interest rate (if we select apples for targeting) or 3% nominal interest rate (if we select bananas). So in this simple example we translated "in kind" difference of inflation (apple inflation vs banana inflation) into difference in the rate of the same inflation. We could as well have 1% inflation target for apples and then we could have 3% nominal interest rate that is the same as natural interest rate for bananas. And since money is neutral, this should not have any impact.

Now however if the natural interest rates of these two possible targets changed randomly we could end up with different nominal interest rate paths based on what commodity we selected as our target. But you claim that this has no impact as long as we consistently hit our target, all other nominal prices will just align themselves to our preferred target (if we selected it correctly). Our problem is not hitting our target. In a way it can be explained as constantly switching our target to a natural interest rate of a different commodity, which means constantly stepping into uncertain territory where our old rules of thumb do not work and that we will introduce real shocks caused by insufficient nominal management that further distorts the outcomes. Or something like that?

PS: I do not know much about this so it is very likely that I got it completely wrong and you are discussing something else entirely. So ignore it if it does not make sense for you and I will just have to learn more about all of it.

Got it, thanks. But then, Sraffa is saying something even more trivial. For smplicity, let's say that 'the' inflation rate is 2% and that consumption tastes are constant. The differential inflation rates of apples and bananas then just means that their supply curves are evolving across time differently. But at any single point of time, they can still be aggregated. So Sraffa is simply denying the concept of an AS curve.

JV: I think you are maybe right. If both apples and banana prices are sticky, and if there are real shocks to the equilibrium relative price of apples and bananas, then it is impossible for monetary policy to get it right, even with perfect knowledge. Is that what you are saying?

That's why the choice of monetary policy target matters, and why it's always a bit of a trade-off, depending on which prices are sticky and what the shocks are.

And yes, choosing the right nominal anchor is essential. For a broad based definition of the numeraire as you are suggesting, I'd say that the numeraire is not consumption, but income or wealth itself. The best targets then are either nominal GDP ala Sumner (or nominal wages, I'd still say) or asset prices ala Farmer, or some combination of the two.

Is there any way to collapse this array of terms? Would you consider that some asset's nominal rate is similar in concept to its own rate? And that the "inflation rate on apples" is equal to the own-rate of apples?

What is the difference between a real rate, a real own rate, a natural rate, and a natural real rate?

david. Yep. But that's OK. If money isn't neutral, or super-neutral, in any sense then natural rates don't exist.

Well, the long-run value of money could just be determined by something else. That theory could have its own equilibrium rate. The what-would-become-the-post-Keynesians, i.e., the Sraffians, tended to have endogenous theories of long-term money that involved either hypothetical real rates on Capital or own-rates on kinds of capital. I don't profess to understand them well enough to provide an account, though.

In terms of the history of thought, the Sraffians were working in a constructionist fashion - i.e., go out there and measure this and measure that, and what manner of optimal equilibrium can you actually compute? This is why they treated the Cambridge capital problem so seriously. As you've noted in a couple of posts recently, a lot of equilibria are circularly defined. But that was precisely the genesis of the Cambridge fight.

We do know now that it is, in fact, impossible to derive representative K with a representative natural real rate r in a gen eq framework of rational individuals; the excess demand function has an arbitrary shape even with identical preferences provided that income is only almost identical. We just don't care. We readily assume that individual market excess demand functions slope downwards nicely globally - a counterfactual which is impossible to ever test, but seems reasonable locally - and if we have that for all capital, then simple arbitrage gives us a representative portfolio of capital. Rational expectations and Arrow securities kick uncertainty to the curb, and so we have a long-term natural rate. The Sraffians never even accepted the first step.

The Austrian-flavoured response, as far as I can tell, hops up and down on the "prices-as-coordinating-mechanism" button to halt efficient arbitrage under intertemporal price distortion, but I defer to Bob here on that field. I think Austrians underestimate the ability of markets and prices to render capital legible enough for the concept of a natural rate to make sense, funnily enough.

Suspend the Samuelsonian device of treating goods over time as distinct. Instead, conceive of a loaf of bread today and tomorrow as the "same" loaf albeit with different value, as conventional English does.

A (nominal) own-rate: the ratio of the price of a good now and the price of the good, invested or stored as people do, after the passage of unit time.

A real own-rate: the ratio of the amount of unit CPI basket that a good is worth now, to the amount of unit hedonically-adjusted CPI basket the good is worth, again after investment or storage, after the passage of unit time.

Nominal and real rates: bundle all goods into representative portfolios. Invoke state-contingent securities to keep the portfolio consistent on an intertemporal basis (or, alternatively, discard uncertainty). Take the own-rate of a unit of this portfolio to give "the" rate.

Natural nominal and real rates: assume investment and storage is done in some optimal market-clearing fashion, in both present and future.

JP: Yep. Reading it over, the whole thing isn't as clear as it should have been. Oh well.

Terminology: remember that a real rate of interest is a nominal rate minus an inflation rate. The question is: which inflation rate? If it's the inflation rate on apples, it's the real rate on apples, which is just another way of saying the "own rate on apples". There's one own rate for each good, and for each basket of goods, etc.

A natural rate is always a real rate. So "natural rate" is just shorthand for "natural real rate". And there's one natural rate for each good, and for each basket of goods, etc.

A natural rate is a theoretical construct that is only defined in a natural rate model. Whether or not it's a useful construct, and how exactly it would be defined, depends on the model. At a minimum, it's got to be some real variable that is independent of the mean level of nominal variables (neutrality), and the mean growth rate of nominal variables (super-neutrality). Otherwise it's best not to talk about "natural rates" at all in that model.

For example, suppose you think that the inflation target matters. That it would be better to target 2% inflation than 3%. Presumably you would say that because you think some real variable (average real menu costs?) would be different at 2% than at 3%. In principle, that means you don't strictly have a natural rate model. If one real thing is different (menu costs) then by the GE principle ("everything depends on everything else") all other real variables will almost certainly depend on the inflation target too. Whether that effect is small enough to ignore, for some real variables, is another question.

david: "Natural nominal and real rates: assume investment and storage is done in some optimal market-clearing fashion, in both present and future."

I disagree with that. The natural rate (of interest, or unemployment, or anything) doesn't have to be optimal, in any sense, or market-clearing. Start with a simple natural rate model, with an optimal market-clearing equilibrium. Add in an externality, or imperfect competition (for example) and the equilibrium is no longer optimal. Add in an efficiency wage theory of unemployment, for example, and it's no longer market-clearing. But it's still a natural rate model. You can still define natural rates that are independent of the mean price level and inflation rate.

Would "as optimal as possible absent factors we discard as transitory" do it? One does need to motivate a "correct" level of intertemporal response.

I dispute that the natural rate is only sensibly defined independent of P(t) and P'(t). Pick your favourite hysteresis model of real output. Or a model with an endogenous money multiplier. Or a model with adaptive expectations, so that NAIRU is the natural rate of unemployment, as Friedman argued - i.e., where P''(t) does matter.

david: You lost me there. Suppose the "long run" Phillips Curve is vertical. Then you can define the natural rate of unemployment as the rate determined by the LRPC. That's regardless of whether that rate is optimal, or distorted by taxes, subsidies, regulations, monopoly power, externalities, whatever. If the LRPC is not vertical, how can you define it?

Noting that "long run" here has nothing to do with the passage of time...

Suppose you have a hysteresis/sunspot model and presently you have a shock - e.g., a simple multiple equilibria model where there is some high-output and low-output equilibrium. Even without any exotic theories of interest rates, the locus of points of consistent long-run inflation and unemployment would entail two vertical lines on the Phillips curve graph. Only one of these could actually turn out to be "the" natural rate of unemployment, plausibly depending on policy taken during the shock, i.e., defined in terms of P(t), P'(t), P''(t), etc. during the t of the shock.

So the natural rate of unemployment can be defined in terms of P and such, yet the intuition of long-run neutrality and superneutrality (i.e., that money illusion has some practical restrictions as a concept) holds. So it makes sense to speak intuitively of a "natural rate", even though nominal variables do matter.

You could object that if we defined a natural rate to disregard nominal variables then by definition this is not, strictly, a natural rate, but this doesn't seem to allow a lot of things that look like natural rates to be labelled as natural rates. NAIRU has P''(t) = 0 right there in the name. If a hyperinflationary central banker set P''(t) ≠ 0 the way actual banks target P'(t) ≠ 0, then the model behind NAIRU implies an equilibrium lower rate of unemployment. Isn't that still a natural rate?

"The question is: which inflation rate? If it's the inflation rate on apples, it's the real rate on apples, which is just another way of saying the "own rate on apples". There's one own rate for each good, and for each basket of goods, etc."

Do you use the same definition as David that an own-rate is equivalent to the difference between a good's spot price and its future price? ie. the reward to storing something? It seems that in David Glasner's most recent that your aren't but I could just be confused:

The old Austrian view on boom/bust cycles is clearly right under a level targetting regime, which the gold standard was. You would get excursions above the target--too many notes in circulation--and then the banks would panic as the gold redemptions started. This is a robust conclusion in an expectations driven world where there is indetermance in when the CB would panic and change the discount rate or collateral rules to claw back the notes.

The recovery of world economies upon breaking with the good standard is somehow taken as a repudiation of the Austrian analysis... But it isn't a repudiation of the model, it is a repudiation of the policy conclusion....

Indeed the context of the debate was this: the gold standard was seen in moral terms as a part of the contract of liberty. You had on one hand people like fisher who saw the gold standard as the problem itself, and then you had the Austrians trying to save the gold standard by pinning the problem on the CBs reaction function. That is, if only the CB did a better job at keeping the level target firm, we wouldn't have these nasty busts. So what is being debated then in the passages you cite: whether it is even feasible for the CB to stabilize policy.

This was a continuation of a debate since the 18th century about equalizing the supply and demand for currency. There was much debate about rules for doing this: the real bills doctrine, the law of reflux, etc... By the 20th century we had already settled on interest rates--particularly the discount rate and reserve requirements, but this policy tool did not seem to work any better. (again enter the Austrian argument: we'll of course it won't work better, you can pick the wrong rate which for a while will cause a boom...)

Hayeks solution was GDP rate targetting.... Mises solution was a money supply target... What we got after the 30s was unemployment targetting.

Scraffa incidentially is actually talking about what we now call AS shocks, and he is saying the the policy targets cannot stabilize AS shocks. We would regard that as right today.... And it doesnt make Hayek wrong in his policy answer; it just makes him (and the Austrians wrong to claim that all booms and busts are Due to CB errors)

In Hayek a "natural rate" is really a valuational relation between production goods producing more or less goods and taking more or less time -- in a model with no money and therefore no actual prices.

The problematic move it to trying to think about these relations in the real world of money and credit and uncertain, taking into account this valuational structure, and attempting to imagine a real world case where this structure is in perfect equilibrium across time yet is instantiations in a money and credit economy.

That is Hayek problematic, the one he discusses most completely in his _Pure Theory of Capital_ (which most people who write on this topic have not read -- a serious issue).